Improvement of invertibility properties of linear operators and branching Lyapunov-Schmidt equation (Q2719466)
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scientific article; zbMATH DE number 1609708
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Improvement of invertibility properties of linear operators and branching Lyapunov-Schmidt equation |
scientific article; zbMATH DE number 1609708 |
Statements
25 June 2001
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solvability of linear equations
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generalized Fredholm operators
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nonlinear equation with parameter
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reduction of the kernel or cokernel
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Improvement of invertibility properties of linear operators and branching Lyapunov-Schmidt equation (English)
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The author considers the problems of solvability of linear equations in linear, normed and Banach spaces. Studied are the linear operator perturbations involving the reduction of the kernel or cokernel being possibly of infinite dimensions. The author introduces the notions of generalized Fredholm operators and establishes conditions of their invertibility. For the branching Lyapunov-Schmidt equation theorems on its reduction with respect to both ``the number of unknowns'' and ``the number of equations'' are obtained.
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